•A reduced model for domain wall dynamics of Néel-wall type is derived.•The front dynamics is driven by the mean curvature and relaxes to a planar interface in the absence of external fields.•The front migration velocity is linearly dependent on the external magnetic field when it is weak.•The results are consistent with Walker’s ansatz. In this paper, we use the matched asymptotic analysis to derive a reduced model for domain wall dynamics within thin films of Néel-wall type in soft ferromagnets. It is found that the front dynamics is driven by mean curvature in the absence of external fields, and always relaxes to a planar interface where the one-dimensional ansatz is valid. The analysis predicts a linear dependence of front migration velocity on the field strength if the external magnetic field is weak, which is consistent with the result of Walker’s ansatz. Moreover, the derivation also identifies a regime where such an analysis fails, which corresponds to the Walker’s breakdown.